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- W2963558765 abstract "We show that the predual of a JBW<inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=Superscript asterisk> <mml:semantics> <mml:msup> <mml:mi /> <mml:mo>∗<!-- ∗ --></mml:mo> </mml:msup> <mml:annotation encoding=application/x-tex>^*</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-triple has the weak Banach-Saks property, that is, reflexive subspaces of a JBW<inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=Superscript asterisk> <mml:semantics> <mml:msup> <mml:mi /> <mml:mo>∗<!-- ∗ --></mml:mo> </mml:msup> <mml:annotation encoding=application/x-tex>^*</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-triple predual are super-reflexive. We also prove that JBW<inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=Superscript asterisk> <mml:semantics> <mml:msup> <mml:mi /> <mml:mo>∗<!-- ∗ --></mml:mo> </mml:msup> <mml:annotation encoding=application/x-tex>^*</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-triple preduals satisfy the Komlós property (which can be considered an abstract version of the weak law of large numbers). The results rely on two previous papers from which we infer the fact that, like in the classical case of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper L Superscript 1> <mml:semantics> <mml:msup> <mml:mi>L</mml:mi> <mml:mn>1</mml:mn> </mml:msup> <mml:annotation encoding=application/x-tex>L^1</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, a subspace of a JBW<inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=Superscript asterisk> <mml:semantics> <mml:msup> <mml:mi /> <mml:mo>∗<!-- ∗ --></mml:mo> </mml:msup> <mml:annotation encoding=application/x-tex>^*</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-triple predual contains <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=script l 1> <mml:semantics> <mml:msub> <mml:mi>ℓ<!-- ℓ --></mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:annotation encoding=application/x-tex>ell _1</mml:annotation> </mml:semantics> </mml:math> </inline-formula> as soon as it contains uniform copies of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=script l 1 Superscript n> <mml:semantics> <mml:msubsup> <mml:mi>ℓ<!-- ℓ --></mml:mi> <mml:mn>1</mml:mn> <mml:mi>n</mml:mi> </mml:msubsup> <mml:annotation encoding=application/x-tex>ell _1^n</mml:annotation> </mml:semantics> </mml:math> </inline-formula>." @default.
- W2963558765 created "2019-07-30" @default.
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- W2963558765 date "2016-07-07" @default.
- W2963558765 modified "2023-10-11" @default.
- W2963558765 title "Weak Banach-Saks property and Komlós’ theorem for preduals of JBW*-triples" @default.
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- W2963558765 doi "https://doi.org/10.1090/proc/13250" @default.
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